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If 7 - 2x ≥ 1, what is the range of x?

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Question: If 7 - 2x ≥ 1, what is the range of x?

Options:

  1. x ≤ 3
  2. x ≥ 3
  3. x < 3
  4. x > 3

Correct Answer: x ≥ 3

Solution: 

7 - 2x ≥ 1 => -2x ≥ -6 => x ≤ 3

If 7 - 2x ≥ 1, what is the range of x?

Practice Questions

Q1
If 7 - 2x ≥ 1, what is the range of x?
  1. x ≤ 3
  2. x ≥ 3
  3. x < 3
  4. x > 3

Questions & Step-by-Step Solutions

If 7 - 2x ≥ 1, what is the range of x?
  • Step 1: Start with the inequality 7 - 2x ≥ 1.
  • Step 2: To isolate the term with x, subtract 7 from both sides: -2x ≥ 1 - 7.
  • Step 3: Simplify the right side: -2x ≥ -6.
  • Step 4: Now, divide both sides by -2. Remember, when you divide by a negative number, you must flip the inequality sign: x ≤ 3.
  • Inequalities – Understanding how to manipulate and solve inequalities, including reversing the inequality sign when multiplying or dividing by a negative number.
  • Algebraic Manipulation – Skills in rearranging equations and isolating variables to find their range.
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